One Dimensional Kinematics (Neon & Corvette ~ Race)

Question

Two cars are travelling at constant speeds. A Neon is travelling at 15.85 m/s and a Corvette is travelling at 26.9 m/s. When a stopwatch is started, the Corvette is 17.5 meters behind the Neon. How long does it take the Corvette to catch the Neon? How far did the Neon travel before it was overtaken?

It took __________ for the Corvette to catch up.

The Neon traveled __________ before it was overtaken.

Answer 1

At time zero, let the x coordinate of the Corvette be x_C = 0.0 and the Neon x_N = 17.5 m ahead of the Corvette. The x coordinates change as follows: x_C = 0 + 26.9 t and x_N = 17.5 + 15.85 t. For them to be at the same x, then 26.9 t = 17.5 + 15.85 t which gives t = 1.58₃₇ seconds. It took 1.58 seconds for the Corvette ...

During this time, the Neon travelled a distance 15.85 t = 25.1 m.